Two projects are included under this heading:1. The estimation and minimization of error in the design cf NMR experiments for chemical analysis, and 2. The calculation of exact representations of probability density functions required for the use of intensity statistics and direct methods for the interpretation of crystallographic data. In the first of these we have analyzed the bias introduced in the estimation of the area under a single peak by the use of apodization filtering. If one does not average over the range of possible bias, but rather considers the worst possible bias induced by an apodizing filter then it is shown that the error induced by the bias can reach 100% or more, depending on the discretizing intervals. In the area of crystallography we have developed the theory required to calculate the probability density functions for crystals with non-symmetric distributions of structure-factor magnitudes. In addition we have begun to examine a variety of possible techniques to correct measurements of low counts which are of the order of magnitude of background noise. The present method simply subtracts the average background which can result in negative counts, which are unphysical. A further part of the project is the writing of an introductory monograph on crystallographic statistics.